Statistical mechanics of ontology based annotations

We present a statistical mechanical theory of the process of annotating an object with terms selected from an ontology. The term selection process is formulated as an ideal lattice gas model, but in a highly structured inhomogeneous field. The model enables us to explain patterns recently observed in real-world annotation data sets, in terms of the underlying graph structure of the ontology. By relating the external field strengths to the information content of each node in the ontology graph, the statistical mechanical model also allows us to propose a number of practical metrics for assessing the quality of both the ontology, and the annotations that arise from its use. Using the statistical mechanical formalism we also study an ensemble of ontologies of differing size and complexity; an analysis not readily performed using real data alone. Focusing on regular tree ontology graphs we uncover a rich set of scaling laws describing the growth in the optimal ontology size as the number of objects being annotated increases. In doing so we provide a further possible measure for assessment of ontologies.